Columbus was funded by the Spanish monarchy (after the Italian government refused to fund him).
Much of the Portuguese voyages of exploration were under the patronage of the kings of that country.
James Cook was a Royal Navy captain.
The voyage that lead Charles Darwin to write "On the Origin of Species" was on boar HMS Beagle, a Royal Navy vessel.
Lewis and Clark were part of the Corps of Discovery, which was part of the US Army.
The spanish gave him three coastel ships due to be scraped.
Portugel was started so they could do those voyages.
If you watched the movie, darwin was on a warship at a time of war. They stopped to get food and water.
Your correct about lewis and clark. But you forget the fur trappers before them at least to the rockies. And you forget the spanish missinaries for the rest of the usa.